Divisible by this year??? (Part 2: Factorials)

Number Theory Level 3

\(n!\) or \(n\)-factorial is the product of all integers from \(1\) up to \(n\) \((n! = 1 \times 2 \times 3 \times ... \times n)\). Find the maximum integral value of \(k\) such that \(2014^k\) divides \(2014!\)

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